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Forced Response of Nonlinear Systems Under Combined Harmonic and Random Excitation

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Nonlinear Structures and Systems, Volume 1

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Abstract

Mechanical systems are often subjected to different types of excitation. In addition to the commonly considered case of deterministic excitation, random excitation or a combination of both types can occur. The authors present a method to calculate periodic probability density functions of nonlinear mechanical systems under combined harmonic and random excitation. During the calculation, the non-stationary Fokker–Planck equation is solved with a Galerkin-type method. The method uses combined orthogonal, time dependent polynomial as well as harmonic correction terms to reshape an initial guess of the probability density function. It can be used to calculate the stochastic behavior of smaller multi-degree of freedom systems. The applicability is demonstrated using different nonlinear mechanical systems, whereby the results of Monte-Carlo simulations validate the method.

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Authors and Affiliations

  1. Institute of Dynamics and Vibration Research, Faculty of Mechanical Engineering, Leibniz University Hannover, Hannover, Germany

    Alwin Förster, Lars Panning-von Scheidt & Jörg Wallaschek

Authors
  1. Alwin Förster
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  2. Lars Panning-von Scheidt
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  3. Jörg Wallaschek
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Corresponding author

Correspondence to Alwin Förster .

Editor information

Editors and Affiliations

  1. Space Structures & Systems Lab., Bldg B52/3, University of Liége, Space, Liége, Belgium

    Gaetan Kerschen

  2. Rice University, Houston, TX, USA

    M. R. W. Brake

  3. University of Bristol, Bristol, UK

    Ludovic Renson

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Förster, A., Scheidt, L.Pv., Wallaschek, J. (2020). Forced Response of Nonlinear Systems Under Combined Harmonic and Random Excitation. In: Kerschen, G., Brake, M., Renson, L. (eds) Nonlinear Structures and Systems, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12391-8_7

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  • DOI: https://doi.org/10.1007/978-3-030-12391-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12390-1

  • Online ISBN: 978-3-030-12391-8

  • eBook Packages: EngineeringEngineering (R0)

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